"With the president tweeting on a regular basis, a daily basis, that the special counsel is conflicted, that he is leading so-called 12 angry Democrats and demeaning and ridiculing him in every way, to be so sanguine about the chances of him being fired is folly for us," Flake said.

Trump in a tweet hours before Flake's request blasted Mueller's probe into Russian election interference and possible collusion between the president's campaign and Moscow as the "angry Mueller gang of Dems" and exclaimed that it is "our Joseph McCarthy era."

"As Justice Scalia explains, we cannot convert an office like this one ... without creating a de facto fourth branch of government fundamentally undermining the principles of the separation of powers that is so core to our liberty," Lee said.

Flake pledged that they would come back to the Senate floor to try to set up the bill for a vote again.

Under the upper chamber's rules, senators can go to the floor to request a vote or passage of any bill or nomination. But any one senator can block their requests.

"We're whipping that to see where people are. I think the leader needs that information to decide how to manage all the competing demands on our time," Cornyn said when asked about discussions within the Republican caucus about the legislation.